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You should be interested in the discussion in

EvansEvans, Gareth A.; Wensley, Christopher D., G.~A. and WensleyComplete involutive rewriting systems, C.~D. {Complete involutive rewriting systems}J. {J Symb. Symbolic Comput.} \textbf{42}~(11 42, No. 11-12), 1034-1051 (2007) 1034--1051. ZBL1128.68044.

on the notion of noncommutative involutive systems, which in the commutative case are a well known modification of the GrobnerGröbner basis theory. Evans' thesis is available at math.RA/0602140math.RA/0602140.

I can't help on the proposed applications.

Ronnie Brown

You should be interested in the discussion in

Evans, G.~A. and Wensley, C.~D. {Complete involutive rewriting systems}. {J. Symbolic Comput.} \textbf{42}~(11-12) (2007) 1034--1051.

on the notion of noncommutative involutive systems, which in the commutative case are a well known modification of the Grobner basis theory. Evans' thesis is available at math.RA/0602140.

I can't help on the proposed applications.

Ronnie Brown

You should be interested in the discussion in

Evans, Gareth A.; Wensley, Christopher D., Complete involutive rewriting systems, J. Symb. Comput. 42, No. 11-12, 1034-1051 (2007). ZBL1128.68044.

on the notion of noncommutative involutive systems, which in the commutative case are a well known modification of the Gröbner basis theory. Evans' thesis is available at math.RA/0602140.

I can't help on the proposed applications.

Ronnie Brown

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Ronnie Brown
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You should be interested in the discussion in

Evans, G.~A. and Wensley, C.~D. {Complete involutive rewriting systems}. {J. Symbolic Comput.} \textbf{42}~(11-12) (2007) 1034--1051.

on the notion of noncommutative involutive systems, which in the commutative case are a well known modification of the Grobner basis theory. Evans' thesis is available at math.RA/0602140.

I can't help on the proposed applications.

Ronnie Brown